In order to unify and extend the results on various fractional integration operators defined and studied during the last three decades, the authors investigate in this paper a pair of new fractional integral operators associated with multivariable

$H$-function due to

*H. M. Srivastava* and

*R. Panda* [J. Reine Angew. Math. 283/284, 265-274 (1976;

Zbl 0318.33006)] and a general class of polynomials introduced by

*H. M. Srivastava* [Indian J. Math. 14, 1-6 (1972;

Zbl 0249.33006)]. Some properties of these operators related to their Mellin transforms are investigated, generalizing the scores of results on various fractional integration operators scattered in the literature.